NEW YORK, May 29 (Reuters) - Oil prices fell on Tuesday, with U.S. crude tumbling nearly 3 percent, on worries that Saudi Arabia and Russia could pump more crude to compensate for a potential supply shortfall, with hedge funds reducing bullish positions in crude.

U.S. West Texas Intermediate (WTI) crude futures slumped $1.83, or 2.7 percent, to $66.05 a barrel.

Saudi Arabia and Russia have discussed raising OPEC and non-OPEC oil production by 1 million barrels per day (bpd) to counter potential supply shortfalls from Venezuela and Iran.

Ahead of the Organization of the Petroleum Exporting Countries’ meeting in Vienna on June 22, concerns that Saudi Arabia and Russia could boost output have exerted downward pressures on oil prices, along with rising production in the United States.

“Market participants remain unsure how quickly an exit strategy can be implemented and whether it will go beyond just balancing the output drop from Venezuela,” said Abhishek Kumar, senior energy analyst at Interfax Energy’s Global Gas Analytics in London.

“They’re worried that the cartel may take a “wait-and-watch” approach on Iran. Consequently, the bearish sentiment is somewhat less prominent on Brent prices.”

The Brent price has fallen nearly 7 percent since hitting $80.50 on May 17, its highest since 2014.

“High uncertainty clouds the short-term outlook and we maintain a neutral view. In the medium to longer term, we still see oil prices falling as indicated by the downward-sloping futures curve. Our ‘low for longer’ view is deferred, not refuted,” Julius Baer’s Norbert Ruecker said in a note.

Hedge funds and other money managers reduced their net long position in Brent and WTI by 169 million barrels over the five weeks to May 22. (tmsnrt.rs/2LBbW8l).

The decision to pare positions in crude points to deeper unease about the sustainability of the rally in oil prices over the last 10 months, said John Kemp, a Reuters market analyst.

Brent now commands its largest premium over U.S. futures in more than three years, meaning U.S. exports are rapidly becoming far more competitive globally than those from northern Europe, Russia or parts of the Middle East.

The spread between Brent and U.S. crude CL-LCO1=R stands at nearly $9 a barrel, its widest since March 2015.

U.S. oil production C-OUT-T-EIA has surged by more than 20 percent in the past two years to 10.73 million bpd. That puts the United States ahead of Saudi Arabia and within reach of top producer Russia, which pumps about 11 million bpd.

Record crude oil volumes from the United States are expected to head to Asia in the coming months, nibbling away the market share of OPEC and Russia. (Additional reporting by Amanda Cooper in London and Jane Chung in Seoul Editing by Marguerita Choy and David Goodman)